This invention relates generally to a frequency rectification system, and, in particular, to a frequency rectification system: apparatus and method using a. Van der Pol Oscillator for rectifying noisy signals for extracting or recovering frequencies of signals that are hidden or buried under noise for monitoring, protecting and/or managing assets including a multifarious grouping of machinery, processes, and instrumentalities.
In signal processing, a signal and its frequency of interest is usually evaluated as a major Fourier transformation component. It is known that in many instances the particular frequency of interest might not be the major Fourier component within an entire frequency range and yet, it still might have the highest amplitude within a certain frequency band. Thus, the frequency of interest is typically obtained by filtering the signal to a certain frequency band surrounding the frequency of interest such that the frequency of interest is the only one or at least, the major one in the spectrum. In such a case, the corresponding spectrum peak and its frequency are easily detected. Thus, in many instances it is possible to initially select a small enough frequency band so that the frequency of interest is associated with a major component within the selected band.
This approach works fine if there is no or little noise in the frequency band that is filtered from the signal and that surrounds the frequency of interest.
However, this approach is problematic in instances when the signal is so noisy that even in the closest proximity to the signal of interest the noise is higher than that of the signal itself. In other words, even if the smallest proximity to the signal of interest is chosen in the spectrum, the signal of interest is completely “buried” under the noise, so that all the spectrum peaks represent those of the noise, rather than of the signal of interest. Hence, in these instances, the signal of interest is too small when compared to the noise and thus, picking a major component will not produce the frequency of interest, but rather a random result.
Hence, there is a need for obtaining a signal of interest from a noisy signal that is so noisy that even in the closest proximity to the signal of interest the noise is higher than that of the signal of interest itself. In other words, there is a need for obtaining a signal of interest that is completely “buried” under noise from a noisy signal comprised of spectrum peaks which represent those of the noise, rather than that of the signal of interest. Moreover, there is a need for solving the problem of obtaining a signal of interest that is “buried” under noise rather than obtaining a random result for monitoring, protecting and/or managing assets including a multifarious grouping of machinery, processes, and instrumentalities.